Problem: What is the sum of all the positive divisors of 91?
Answer: The prime factorization of $91$ is $7 \cdot 13$. It follows that the sum of the divisors of $91$ is equal to $(1 + 7)(1 + 13)$, as each factor of $91$ is represented when the product is expanded. It follows that the answer is equal to $(1 + 7)(1 + 13) = (8)(14)$, or $\boxed{112}$.